Magnetic test of the elliptically
polarizing undulator for SPEAR BL05
Final testing
June 2012
Danfysik A/S
Gregersensvej 8
2630 Taastrup
Denmark
Table of Contents
Table of Contents ......................................................................................................................................... 2
Introduction .............................................................................................................................................. 3
A. Reproducibility of Hall probe bench ............................................................................................. 4
B. Reproducibility of the integrating coil .......................................................................................... 7
C. Magnetic alignment using the Hall probe and field roll-off ......................................................10
Magnetic Measurements without tunecorrectors....................................................................................12
D. Hall probe scans on the undulator axis ......................................................................................12
E. Summarizing table of Hall results ................................................................................................19
F. The first integrals ...........................................................................................................................21
G. First derivative of the first integrals ............................................................................................38
H. The second integrals .....................................................................................................................49
Magnetic Measurements with tunecorrectors .........................................................................................59
I.
First integral scans after tune shim installation .........................................................................60
J.
Hall probe scans on the undulator axis(13 mm gap) ...............................................................65
K. Analysis of peak field rolloff..........................................................................................................67
L.
Reproducibility of the magnetic array .........................................................................................68
M. Correction coils HP mode ..............................................................................................................72
General Comments......................................................................................................................................74
N. Mounting of the permanent magnets and the shimming process ..........................................74
O. Conclusion .......................................................................................................................................77
2
Introduction
We report the results of the magnetic measurements carried out at Danfysik of the 2m EPU for
the SPEAR BL05 at SSRL. The measurements were carried out using the Danfysik A/S Hall probe
bench and flip coil bench. The resolution of the measurements at 13 mm gap is investigated in
Section A of this report. The parameters for the measurements are given below:
Length of Hall probe scans
Distance between measuring points
Length of flip coil
Diameter of flip coil
Number of turns in flip coil
Interval measured by the flip coil
Distance between flip coil measurement points
3300 mm
1 mm
3500 mm
5.5 mm
20
|x| ≤ 25 mm
1 mm
The (x, y, z) coordinate system used in this report has the z-direction in the beam direction. In
the raw data files it is, however, labeled as (x, z, s) where z is the vertical and s the longitudinal
component.
The Hall probe scans were analyzed using the B2E program from ESRF based on the Igor Pro
software. An additional set of macros has been written at Danfysik which makes use of the B2E
program for the data analysis and then produces the result graphs. Nearly all the graphs
presented in this report are made with these macros. The Hall probes were calibrated using a
calibration magnet with a NMR probe as reference, as described in a separate calibration report.
The calibration range is from –1.8 T to 1.8 T. For this device, we had to design a special probe,
which allowed for the calibration of the horizontal probe, up to 1 T.
From the Hall probe measurements we get:
Period length
139.98 mm ( 0.01 mm)
Total number of poles(including endpoles)
31
Measurements were carried out for gap sizes of 13,20,30,40, and 120 mm
In Section A and B of this report the resolution of the measurement equipment is investigated.
Section C concerns the alignment of the undulator and the measurement equipment. Section D
contains a summary of the on-axis measurements with the Hall probe, as obtained for the device
without tune correctors installed.
The integrated multipoles and the second integrals as a
function of the x-position was measured with the flip coil and the results of the analysis can be
found in Sections F,G, and H. In sections I and J, the magnetic results for the device after
tuneshim installation are shown. We have performed some mechanical hysteresis tests, and the
results of these are shown in section L.
General comments and information on the mounting of the permanent magnets on the undulator
and the shimming procedure is given in Section N. Finally a conclusion is given in Section O.
3
A. Reproducibility of Hall probe bench
The reproducibility of the measurement equipment is investigated using the five on-axis Hall
probe measurements in the HP Mode and the flip coil measurements at 13 mm gap.
The 13 mm gap was chosen to check the reproducibility of the Hall probe bench as the gradients
are largest at the minimum gap and the effects of differences between the real and recorded Hall
probe position will be maximum. Such differences might occur due to the resolution in the
Heidenhain ruler used to read the Hall probe position, vibration in the timing belt used to move
the probe and non-linearity in the rails used to guide the probe. Five Hall probe scans have been
done under identical conditions and analyzed individually. In the Figure 1 to Figure 5, each of the
scans is identified with a separate color.
Figure 1 shows the vertical angle for a 3 GeV electron. The reproducibility is good due to the
small value of the transverse field on the undulator axis. The reproducibility in the horizontal
angle averaged over one period is shown in Figure 2. The fine structure is well reproduced from
scan to scan. The values agree at the start and end of the scans because of the normalization to
the flip coil values for the first integral, and in the middle of the undulator there is only up to
about 2 radian difference between the highest and lowest scan.
The orbits are shown in Figure 3 and Figure 4. Both the vertical and horizontal orbit reproduces
well and the spread in the orbit walk is around than 0.5 m for the vertical orbit and 1.3 m for
the horizontal orbit. The phase angle error at each pole is shown in Figure 5.
Electron angle, av. one period (rad)
15
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
10
5
0
-5
-10
-15µrd
0.0
0.5
1.0
1.5
2.0
Longitudinal position (m)
2.5
3.0
Figure 1 The vertical electron angle as obtained from 5 hall probe scans measured at
13 mm gap, in the HP mode for x=0 and y=0.
4
Electron angle, av. one period (rad)
300
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
200
100
0
-100
-200
-300µrd
0.0
0.5
1.0
1.5
2.0
Longitudinal position (m)
2.5
3.0
Figure 2 The horizontal electron angle, averaged over on undulator period, as
obtained from 5 hall probe scans measured at 13 mm gap, in the HP mode, for x=0
and y=0.
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
6µm
Horizontal orbit walk (m)
5
4
3
2
1
0
-1
-2
-3
-4
-5
0.0
0.4
0.8
1.2
1.6
2.0
Longitudinal position (m)
2.4
2.8
3.2
Figure 3 Vertical orbit walk from 5 hall probe scans measured at 13 mm gap, in the
HP mode, for x=0 and y=0.
5
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
Electron angle, av. one period
40µm
20
0
-20
-40
0.0
0.5
1.0
1.5
2.0
Longitudinal position (m)
2.5
3.0
Figure 4 . Horizontal orbit walk from 5 hall probe scans measured at 13 mm gap, in
the HP mode, for x=0 and y=0.
80
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
Phase angle error (degrees)
60
40
20
0
-20
-40
-60
-80
0
5
10
15
Pole number
20
25
30
Figure 5 Phase angle error calculated from 5 hall probe scans measured at 13 mm
gap, in the HP mode for x=0 and y=0.
6
B. Reproducibility of the integrating coil
The reproducibility of the flip coil has been determined from five normal and five twisted coil scans
measured at 13 mm gap
First Integral
10
80
60
40
20
6
0
4
-20
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
Limits
Ix Std. Dev.
-40
-60
-80
First Integral Horizontal [Gcm]
First Integral Horizontal [Gcm]
8
2
0
-25
-15
-20
-10
0
-5
5
10
15
20
25
Transverse Position [cm]
Figure 6 Reproducibility of the horizontal 1st field integral, from the flip coil
8
130
120
6
100
First Integral Vertical [Gcm]
First Integral Vertical [Gcm]
110
90
80
70
4
60
50
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
IzStDev
Neglimits
40
30
20
2
10
0
-25
-20
-15
-10
-5
0
5
10
15
20
Transverse Position [cm]
Figure 7 Reproducibility of the vertica 1st field integral, from the flip coil
7
25
Second integral
500
8000
400
4000
2000
300
0
200
-2000
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
Limits
JxStDev
-4000
-6000
-8000
100
Second Integral Horizontal [Gcm^2]
Second Integral Horizontal [Gcm^2]
6000
0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
Transverse Position [cm]
Figure 8 Reproducibility of the horizontal 2nd field integral, from the flip coil.
500
8000
400
4000
2000
300
0
200
-2000
Scan 1
Scan 2
Scan 3
Scan 4
Scan 5
Limits
JxStDev
-4000
-6000
-8000
100
0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Transverse Position [cm]
Figure 9 Reproducibility of the vertical 2nd field integral, from the flip coil.
8
2.5
Second Integral Horizontal [Gcm^2]
Second Integral Horizontal [Gcm^2]
6000
9
C. Magnetic alignment using the Hall probe and field roll-off
The vertical position of the median plane was measured for each horizontal pole at 50 mm gap
by making Hall probe scans at y = -10, -5, 0, 10 and 5 mm, with the device placed in the CP
mode. The horizontal position was determined from Hall scans at x = -20, -10, 0, 10, 20 mm.
The scans were analyzed using an Igor Pro macro, which fits a parabola to the measured peak
field values for each pole and determines the y (or x) position of the minimum and the fit error.
The data are plotted as a function of the pole number and a line is fitted to the data giving the
position of the mid plane. The first and last two poles are excluded from the fit. The parameters
of the line fit:
y = A + B*(Pole #) or
x = A + B*(Pole #)
are given in Table B1 and B2. The scattering of the magnetic center positions is primarily due to
the internal inhomogeneity of the magnetic blocks and cannot be avoided, unless actions are
taken to physically correct this by transverse shift of the magnets. The observed scattering is
very reproducible and the uncertainties on the linear fit parameters are relatively small. The
uncertainty on each pole center as determined from the polynomial fit is indicated in the graphs
by the error bars (not including uncertainty on the measurements). The parameters for the
horizontal and vertical position of the undulator mid-plane are given in Tables B1 and B2. These
results show that we have a good alignment of the Hall probe is traveling with respect to the
optimal magnetic center axis of the device.
Table B1. Parameters for the horizontal position of the undulator mid plane.
Gap (mm)
50
A (mm)
-0.08 ± 0.1
B (mm/pole #)
0.00 ± 0.00
Center off-set (mm)
-0.0312
Table B2. Parameters for the vertical position of the undulator mid plane.
Gap (mm)
50
A (mm)
0.01± 0.06
B (mm/pole #)
0.003 ± 0.00
10
Center off-set (mm)
-0.03
2.0
X-scan for y = __ at 50 mm gap. The solid line is a fit with x(s)=A+B*Pol#:
A= -0.085+-0.114 mm; B =0.004+-0.007 mm
Transverse pole center position (mm)
1.5
1.0
Pitch from pole 2 to 28 is:0.0998+-0.1887mm, Offset is-0.0312mm
0.5
0.0
-0.5
-1.0
-1.5
-2.0
0
2
4
6
8
10
12
14 16 18
Pole number
20
22
24
26
28
Figure 10 Horizontal alignment analysis
2.0
Y-scan for x =__ at 50 mm gap. The solid line is a fit with y(s)=A+B*Pol#:
A= 0.01+-0.058 mm; B =-0.003+-0.003 mm
Vertical pole center position (mm)
1.5
1.0
Pitch from pole 2 to 17 is:-0.0755+-0.0959mm, Offset is-0.03mm
0.5
0.0
-0.5
-1.0
-1.5
-2.0
0
2
4
6
8
10
12
14 16 18
Pole number
Figure 11 Vertical alignment analysis
11
20
22
24
26
28
30
30
Magnetic Measurements without tunecorrectors
The first part of the measurement programme, concerns the magnetic measurements of the
device without tuneshims.
D. Hall probe scans on the undulator axis
HP Mode: 13 mm gap
Two hall probe scans along the center axis of the device have been measured at 13 mm gap, in
each of the 4 modes. The data is analyzed with B2E in Igor Pro using a macro made by
Danfysik. The Igor Pro files are saved together with the data files.
From the VP hall probe scans we obtain an average period length of u = 139.98±0.001mm from
the position of the 1. harmonic in the Fourier transformed of the horizontal field data.
The following figures show the field components, electron angle and orbits, vertical peak field of
the poles and phase error at each pole, obtained from a Hall probe scan at 13 mm gap on the
center line.
1.0
0.8
Gap = 13 mm: HP mode
Vertical magnetic field
Vertical field (T)
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Figure 12 The By-component of the magnetic field at 13 mm gap for x = y = 0(HP
Mode).
12
15
10
Gap = 13 mm: HP mode
Horizontal magnetic field
Vertical field (T)
5
0
-5
-10
-15x10
-3
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Electron angles averaged over a period (mrd)
Figure 13 The Bx-component of the magnetic field at 16 mm gap for x = y = 0(HP
Mode).
400
Gap = 13 mm: HP mode
Horizontal average angle
Vertical average angle
300
200
100
0
-100
-200
-300
-400µrd
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Figure 14 The electron angles, averaged over on undulator period, at 13 mm gap for x
= y = 0(HP Mode).
13
Figure 15 The electron orbits for a 3 GeV electron at 13 mm gap for x = y = 0(HP
Mode).. The horizontal orbit averaged over one undulator period is also shown.
12
Gap = 13 mm: HP mode
Phase Error
Phase error (degree)
8
4
0
-4
-8
-12
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Pole number
Figure 16 The phase error from vertical field as a function of pole number for x=0 and
y=0(HP Mode), at 13 mm gap
14
2
Flux (Photon/s/0.1% bandwidth/mrad /A)
14x10
15
Gap = 13 mm: HP mode
Flux
FFT_368tht
12
10
8
6
4
2
0
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Energy (keV)
Figure 17 The calculated flux spectra compared with the case of a perfect planar
undulator without phase error.(HP Mode)
15
CP+ Mode: 13 mm gap
0.7
Gap = 13 mm: CP+ mode
Horizontal magnetic field
Vertical magnetic field
0.6
0.5
0.4
0.3
Electron orbits
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
Longitudinal position (m)
Figure 18 The Bx- and By-component of the magnetic field at 13 mm gap, for
x=y=0(CP+ mode)
50
40
30
Gap = 13 mm: CP+ mode
Vertical orbit
Horizontal orbit
Electron orbits
20
10
0
-10
-20
-30
-40
-50µm
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Figure 19 The electron orbits for a 3 GeV electron at 13 mm gap for x = y = 0(CP+
Mode).. The horizontal orbit averaged over one undulator period is also shown.
16
CP- Mode: 13 mm gap
0.7
0.6
0.5
Gap = 13 mm: CP- mode
Horizontal magnetic field
Vertical magnetic field
0.4
0.3
Electron orbits
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Figure 20 The Bx- and By-component of the magnetic field at 13 mm gap, for
x=y=0(CP- mode)
50
40
30
Gap = 13 mm: CP- mode
Vertical orbit
Horizontal orbit
Electron orbits
20
10
0
-10
-20
-30
-40
-50µm
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Figure 21: The electron orbits for a 3 GeV electron at 13 mm gap for x = y = 0(CPMode).. The horizontal orbit averaged over one undulator period is also shown.
17
VP Mode( 30 mm gap)
0.6
Horizontal field (T)
0.4
Gap = 13 mm: VP mode
Horizontal magnetic field
0.2
0.0
-0.2
-0.4
-0.6
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Figure 22 The Bx-component of the magnetic field at 16 mm gap for x = y = 0(VP
Mode).
Figure 23 The electron orbits for a 3 GeV electron at 13 mm gap for x = y = 0(VP
Mode).. The horizontal orbit averaged over one undulator period is also shown.
18
E. Summarizing table of Hall results
Table 1 Gap summary for the HP mode
On
axis
Gap
13
20
30
40
Ix
Iy
Jx
Jy
Bz_peak
RMS(Bz)
Ephoton
Gm
Gm
Gm^2
Gm^2
T
Degrees
eV
-0.4
-0.26
-0.17
-0.1
0.28
0.26
0.22
0.2
0.1374
0.3634
0.4234
0.4951
-0.4028
-0.4481
-0.3461
-0.2781
0.9015
0.7917
0.6436
0.5129
2.95
2.77
2.71
2.75
7.662
10.341
16.231
25.664
0
0
0.4544
-0.2220
0.0727
2.79
417.918
120
Table 2 Gap summary for CP+ mode
On
axis
Gap
13
20
30
40
120
Ix
Iy
Gm
Gm
0.02
-0.04
-0.04
-0.08
0.01
1.04
0.86
0.74
0.73
0.11
Jx
Jy
Gm^2
Gm^2
1.6457
0.8960
0.5360
0.2816
0.4485
Bz_peak
Bx_peak
Ephoton
T
T
eV
1.3214
0.8425
0.5636
0.7201
0.0341
0.7335
0.5553
0.3886
0.2754
0.0209
0.7317
0.5549
0.3866
0.2745
0.0211
7.401
11.970
23.163
43.915
564.026
Table 3 Gap summary for CP- mode
On
axis
Gap
13
20
30
40
120
Ix
Iy
Gm
Gm
-0.24
-0.04
0.03
0
-0.03
0.51
0.57
0.6
0.51
0.12
Jx
Jy
Gm^2
Gm^2
0.0641
0.9012
1.2141
1.0361
0.5176
0.1678
0.1090
0.2200
0.2367
0.1262
Bz_peak
Bx_peak
Ephoton
T
T
eV
0.7321
0.5539
0.3878
0.2750
0.0209
0.7335
0.5557
0.3872
0.2748
0.0211
7.395
11.971
23.163
43.932
563.957
Bx_peak
T
RMS(Bx)
Degrees
Ephoton
eV
0.4744
4.08
30.067
Table 4 Gap summary for VP mode
On
axis
Gap
30
Ix
Gm
-0.03
Iy
Gm
Jx
Gm^2
0.38
0.9492
Jy
Gm^2
0.0192
19
20
F. The first integrals
The normal and skew first integrals have been measured in the interval –2.5  x  2.5 cm in 0.1
cm steps with the flip coil at the specified phases at 13 mm gap, and at increasing gaps. Using an
Igor Pro macro the averages of the measured field integrals were calculated. The data were
then converted from Gm to Gcm and the x-positions converted from mm to cm.
Multipole
analysis was carried out for this device, and limits were imposed on the multipole content within
a  25 mm window. As we can see from Table 5 to Table 8, the multipole content is outside
these limits at some of the chosen phases, only at minimum gap.
In the following figures, the first integrals are presented for the 4 phases at 13 mm gap, as well
as the first integrals for the HP mode at increasing gaps. We see that, as the magnetic gap is
increased, the integrals decay rapidly. Included in the graphs are the polynomial fits, which
which we can deduce the multipole content. At minimum gap, the multipoles are just outside the
specification, due to a rapid field integral variation near the undulator axis.
250
Phase = HP
Ix,
Iy,
200
First Integrals (Gcm)
150
Gap = 13
Fit of Ix
Fit of Iy
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 24 First integrals. 13 mm gap. HP mode
21
1.0
1.5
2.0
2.5
250
Phase = HP
Ix,
Iy,
200
150
Gap = 20
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.5
2.0
2.5
Transverse position (cm)
Figure 25 First integrals. 20mm gap. HP mode
250
Phase = HP
Ix,
Iy,
200
150
Gap = 30
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 26: First integrals. 30mm gap. HP mode
22
1.0
250
Phase = HP
Ix,
Iy,
200
150
Gap = 40
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.5
2.0
2.5
Transverse position (cm)
Figure 27 First integrals. 40mm gap. HP mode
250
Phase = HP
Ix,
Iy,
200
150
Gap = 120
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 28 First integrals.120mm gap. HP mode
23
1.0
Table 5: Multipoles at increasing gaps in HP mode.
Gap
(mm)
Mode
13
HP
Gap
(mm)
Mode
20
HP
Gap
(mm)
Mode
30
HP
Gap
(mm)
Mode
40
HP
Gap
(mm)
120
Gap
(mm)
120
Mode
HP
Mode
HP
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole (G/cm^3)
12-pole(G/cm^4)
Skew
-33.9
65.5
10.7
-50.4
5.4
14.6
Skew error
2.4
5.4
10.8
9.5
12.5
5.3
Normal
27.9
-78.4
93.3
67.3
-59.5
-26.3
Normal
error
2.4
5.6
11.1
9.8
12.9
5.5
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-28.4
26.4
14.0
-7.5
-0.6
Skew error
0.7
1.1
0.7
0.7
0.1
Normal
39.7
-21.9
4.7
7.6
-0.8
Normal
error
1.3
2.0
1.2
1.2
0.2
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-20.5
12.6
10.2
-2.0
-0.6
Skew error
0.3
0.3
0.3
0.1
0.1
Normal
29.7
-4.6
2.1
-0.8
-0.4
Normal
error
0.4
0.3
0.4
0.1
0.1
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-9.4
6.6
6.4
-1.8
-0.4
Skew error
0.2
0.2
0.2
0.0
0.0
Normal
24.4
-4.3
1.3
-0.6
-0.2
Normal
error
0.1
0.1
0.1
0.0
0.0
Multipole
2-pole (Gcm)
Skew
0.0
-0.0
Skew error
0.0
0.0
Normal
0.0
-0.0
Normal
error
0.0
0.0
0.0
0.0
-0.0
0.0
0.0
0.0
-0.0
0.0
0.0
0.0
0.0
0.0
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
24
250
Phase = CP+ Gap = 13mm
Ix,
Fit of Ix
Iy,
Fit of Iy
200
150
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.5
2.0
2.5
Transverse position (cm)
Figure 29 First integrals. 13 mm gap. CP+ mode
250
Phase = CP+ Gap = 20mm
Ix,
Fit of Ix
Iy,
Fit of Iy
200
150
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 30 First integrals. 20 mm gap. CP+ mode
25
1.0
250
Phase = CP+ Gap = 30mm
Ix,
Fit of Ix
Iy,
Fit of Iy
200
150
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.5
2.0
2.5
Transverse position (cm)
Figure 31 First integrals. 30 mm gap. CP+ mode
250
Phase = CP+ Gap = 40mm
Ix,
Fit of Ix
Iy,
Fit of Iy
200
150
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 32: First integrals. 40 mm gap. CP+ mode
26
1.0
250
Phase = CP+ Gap = 120mm
Ix,
Fit of Ix
Iy,
Fit of Iy
200
150
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 33 First integrals. 120 mm gap. CP+ mode
27
1.0
1.5
2.0
2.5
Table 6: Multipoles at increasing gaps in CP+ mode.
Gap
(mm)
Mode
13
CP+
Gap
(mm)
Mode
20
CP+
Gap
(mm)
Mode
30
CP+
Gap
(mm)
Mode
40
CP+
Gap
(mm)
120
Gap
(mm)
120
Mode
HP
Mode
CP+
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole (G/cm^3)
12-pole(G/cm^4)
Skew
-10.3
16.2
51.0
-48.8
-53.7
22.5
Skew error
1.7
3.9
7.9
7.0
9.2
3.9
Normal
51.4
-22.2
102.9
49.2
-85.0
-22.2
Normal
error
2.3
5.2
10.3
9.1
12.0
5.1
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-8.7
-13.6
5.1
2.4
0.0
Skew error
0.5
0.5
0.5
0.1
0.1
Normal
74.8
17.8
-9.4
-3.2
0.3
Normal
error
1.3
1.2
1.3
0.3
0.2
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-7.2
-9.2
5.6
0.5
-0.3
Skew error
0.2
0.2
0.2
0.0
0.0
Normal
68.7
14.1
-7.3
-2.7
0.4
Normal
error
0.2
0.2
0.2
0.0
0.0
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-2.6
-6.8
4.8
-0.4
-0.3
Skew error
0.1
0.1
0.1
0.0
0.0
Normal
58.6
9.1
-5.4
-1.9
0.3
Normal
error
0.2
0.2
0.2
0.0
0.0
Skew
-1.1
-0.7
Skew error
0.1
0.1
Normal
18.5
2.1
Normal
error
0.1
0.0
-0.1
0.0
-0.0
0.1
0.0
0.0
-0.2
-0.1
-0.0
0.1
0.0
0.0
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
28
250
Phase = CPIx,
Iy,
200
150
Gap = 13mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 34 First integrals. 13 mm gap. CP- mode
29
1.0
1.5
2.0
2.5
250
Phase = CPIx,
Iy,
200
150
Gap = 20mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.5
2.0
2.5
Transverse position (cm)
Figure 35 First integrals. 20 mm gap. CP- mode
250
Phase = CPIx,
Iy,
200
150
Gap = 30mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 36 First integrals. 30 mm gap. CP- mode
30
1.0
250
Phase = CPIx,
Iy,
200
150
Gap = 40mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 37 First integrals. 40 mm gap. CP- mode
31
1.0
1.5
2.0
2.5
250
Phase = CPIx,
Iy,
200
150
Gap = 120mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 38 First integrals. 120 mm gap. CP- mode
32
1.0
1.5
2.0
2.5
Table 7: Multipoles at increasing gaps in CP- mode.
Gap
(mm)
Mode
13
CP-
Gap
(mm)
Mode
20
CP-
Gap
(mm)
Mode
30
CP-
Gap
(mm)
Mode
40
CP-
Gap
(mm)
Mode
120
CP-
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole (G/cm^3)
12-pole(G/cm^4)
Skew
-8.8
12.1
-94.6
9.3
89.3
-8.8
Skew error
3.6
8.2
16.4
14.5
19.1
8.1
Normal
104.2
14.4
-38.0
-0.0
5.7
-1.0
Normal
error
-8.8
12.1
-94.6
9.3
89.3
-8.8
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-11.4
9.4
3.6
-0.0
0.8
Skew error
1.1
1.0
1.1
0.2
0.2
Normal
89.5
14.8
-27.8
-3.3
2.7
Normal
error
0.4
0.4
0.4
0.1
0.1
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-5.8
5.4
5.5
-0.7
-0.1
Skew error
0.3
0.2
0.3
0.1
0.0
Normal
74.1
13.9
-16.4
-2.7
1.4
Normal
error
0.2
0.2
0.2
0.0
0.0
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
1.7
2.1
4.7
-1.0
-0.3
Skew error
0.1
0.1
0.1
0.0
0.0
Normal
61.7
6.5
-8.6
-1.7
0.6
Normal
error
0.2
0.2
0.2
0.0
0.0
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
2.9
0.2
-0.3
-0.1
0.0
Skew error
0.1
0.1
0.1
0.0
0.0
Normal
16.3
1.9
-0.3
-0.2
-0.0
Normal
error
0.1
0.1
0.1
0.0
0.0
33
250
Phase = VP
Ix,
Iy,
200
150
Gap = 13mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.5
2.0
2.5
Transverse position (cm)
Figure 39 First integrals. 13 mm gap. VP mode
250
Phase = VP
Ix,
Iy,
200
150
Gap = 20mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 40 First integrals. 20 mm gap. VP mode
34
1.0
250
Phase = VP
Ix,
Iy,
200
150
Gap = 30mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
1.5
2.0
2.5
Transverse position (cm)
Figure 41 First integrals. 30 mm gap. VP mode
250
Phase = VP
Ix,
Iy,
200
150
Gap = 40mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 42 First integrals. 40 mm gap. VP mode
35
1.0
250
Phase = VP
Ix,
Iy,
200
150
Gap = 120mm
Fit of Ix
Fit of Iy
First Integrals (Gcm)
100
50
0
-50
-100
-150
-200
-250
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
Transverse position (cm)
Figure 43 First integrals. 40 mm gap. VP mode
36
1.0
1.5
2.0
2.5
Table 8 Multipoles at increasing gaps in CP- mode.
Gap
(mm)
Mode
13
VP
Gap
(mm)
Mode
20
VP
Gap
(mm)
Mode
30
VP
Gap
(mm)
Mode
40
VP
Gap
(mm)
Mode
120
VP
Skew
-14.0
-23.6
-12.6
-8.6
7.7
6.6
Skew error
1.9
4.4
8.8
7.8
10.3
4.4
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-21.6
-15.5
10.8
2.8
-0.4
Skew error
0.6
0.5
0.5
0.1
0.1
Normal
59.6
47.0
-6.0
-6.8
0.2
Normal
error
1.1
1.0
1.1
0.2
0.2
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-9.2
-9.0
8.1
1.7
-0.5
Skew error
0.1
0.2
0.1
0.1
0.0
Normal
53.1
24.1
-1.7
-5.7
-0.0
Normal
error
0.2
0.4
0.2
0.2
0.0
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-2.0
-5.9
4.9
-0.3
-0.3
Skew error
0.1
0.1
0.1
0.0
0.0
Normal
51.9
10.3
-1.4
-2.0
-0.0
Normal
error
0.2
0.2
0.2
0.0
0.0
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole
(G/cm^3)
Skew
-2.2
-0.8
0.1
0.1
-0.0
Skew error
0.1
0.1
0.1
0.0
0.0
Normal
18.9
1.1
-0.0
0.0
-0.0
Normal
error
0.0
0.0
0.0
0.0
0.0
37
Normal
60.5
99.6
44.1
-37.3
-42.6
10.9
Normal
error
1.5
3.3
6.6
5.9
7.7
3.3
Multipole
2-pole (Gcm)
4-pole (G)
6-pole (G/cm)
8-pole (G/cm^2)
10-pole (G/cm^3)
12-pole(G/cm^4)
G. First derivative of the first integrals
The first derivative of the first integrals has been computed from the polynomial fit of the first
integral, where a sufficient high number of polynomial terms has been used, to achieve
convergence.
500
Phase = HP Gap = 13 mm
Skew integral
Normal integral
400
Derivative of first integral (G)
300
200
100
0
-100
-200
-300
-400
-500
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 44 First derivative of the first integral.13 mm gap, HP Mode.
38
2.0
2.5
400
Phase = HP Gap = 20
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
Transverse position (cm)
Figure 45 First derivative of the first integral.20 mm gap, HP Mode.
400
Phase = HP Gap = 30
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 46 First derivative of the first integral.30 mm gap, HP Mode.
39
2.0
2.5
400
Phase = HP Gap = 40
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0
2.5
Transverse position (cm)
Figure 47 First derivative of the first integral.40 mm gap, HP Mode.
400
Phase = HP Gap = 120
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 48 First derivative of the first integral.120 mm gap, HP Mode.
40
400
Phase = CP+ Gap = 13
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 49 First derivative of the first integral.13 mm gap, CP+ Mode.
41
2.0
2.5
400
Phase = CP+ Gap = 20
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0
2.5
Transverse position (cm)
Figure 50 First derivative of the first integral.20 mm gap, CP+ Mode.
400
Phase = CP+ Gap = 30
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 51 First derivative of the first integral.30 mm gap, CP+ Mode.
42
400
Phase = CP+ Gap = 40
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0
2.5
Transverse position (cm)
Figure 52 First derivative of the first integral.40 mm gap, CP+ Mode.
400
Phase = CP+ Gap = 120
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 53 First derivative of the first integral.40 mm gap, CP+ Mode.
43
400
Phase = CP- Gap = 13
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0
2.5
Transverse position (cm)
Figure 54 First derivative of the first integral.13 mm gap, CP- Mode.
400
Phase = CP- Gap = 20
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 55 First derivative of the first integral.20 mm gap, CP- Mode.
44
400
Phase = CP- Gap = 30
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0
2.5
Transverse position (cm)
Figure 56 First derivative of the first integral.30 mm gap, CP- Mode.
400
Phase = CP- Gap = 40
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 57 First derivative of the first integral.40 mm gap, CP- Mode.
45
400
Phase = CP- Gap = 120
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0
2.5
Transverse position (cm)
Figure 58 First derivative of the first integral.120 mm gap, CP- Mode.
400
Phase = VP Gap = 13
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 59 First derivative of the first integral.13 mm gap, VP Mode.
46
400
Phase = VP Gap = 20
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0
2.5
Transverse position (cm)
Figure 60 First derivative of the first integral.20 mm gap, VP Mode.
400
Phase = VP Gap = 30
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 61 First derivative of the first integral.30 mm gap, VP Mode.
47
400
Phase = VP Gap = 40
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
2.0
2.5
Transverse position (cm)
Figure 62 First derivative of the first integral.40 mm gap, VP Mode.
400
Phase = VP Gap = 120
Skew integral
Normal integral
300
Derivative of first integral (G)
200
100
0
-100
-200
-300
-400
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Transverse position (cm)
Figure 63 First derivative of the first integral.120 mm gap, VP Mode.
48
H. The second integrals
The second integrals were measured by performing both twisted and normal flip coil turn
measurements at all gaps. The second integrals Jx and Jy can be calculated from the
measurements with twisted flip coil and the measurements of the first integrals
A normal and a twisted flip quick coil scan have been measured in the y=0 plane over the
interval –2.5  x  2.5 cm with 0.2 cm steps at each gap. The data analysis is done with an Igor
Pro macro that loads the first integral and second integral data files, converts the length unit to
centimeters and calculates the average second integrals at each x-position. Our standard
procedure is to correct the first and second field integrals by subtracting of the ambient field
integral contribution. This was chosen to be at open gap (120 mm). In the CP- mode, at 13 mm
gap, the horizontal second field integral, is just outside the specification.
Figure 64 Second integrals. 13 mm gap. HP mode
49
Figure 65 Second integrals. 20 mm gap. HP mode
Figure 66 Second integrals. 30 mm gap. HP mode
50
Figure 67 Second integrals. 30 mm gap. HP mode
Figure 68 Second integrals. 120 mm gap. HP mode
51
Figure 69 Second integrals. 13 mm gap. CP+ mode
Figure 70 Second integrals. 20 mm gap. CP+ mode
52
Figure 71 Second integrals. 30 mm gap. CP+ mode
Figure 72 Second integrals. 40 mm gap. CP+ mode
53
Figure 73 Second integrals. 120 mm gap. CP+ mode
Figure 74 Second integrals. 13 mm gap. CP- mode
54
Figure 75 Second integrals. 20 mm gap. CP- mode
Figure 76 Second integrals. 30 mm gap. CP- mode
55
Figure 77 Second integrals. 40 mm gap. CP- mode
Figure 78 Second integrals. 120 mm gap. CP- mode
56
Figure 79 Second integrals. 13 mm gap. VP mode
Figure 80 Second integrals 20 mm gap. VP mode
57
Figure 81 Second integrals 30 mm gap. VP mode
Figure 82 Second integrals 40 mm gap. VP mode
58
Figure 83 Second integrals 40 mm gap. VP mode
Magnetic Measurements with tunecorrectors
In this section, magnetic measurements are presented for the device, after ESRF-style tune
correctors have been installed. 4 sets of shims were installed, 16 individual shims in all.
In this section we will present integral and hall scans for the 4 interesting phases, at minimum
gap, as well as flip-coil measurements at the same phases.
The resultant first integrals, defined as the sum of the measured, and dynamic integrals, was
optimized to be smallest in the circular phases at minimum gap. In the HP mode, the effect of
the shims actually worsens the resultant integral. In the VP mode, the shims also reduce the
resultant dynamic integrals. At 30 mm gap, the HP mode and VP mode are manageable.
As expected, there was no drastic effect on the undulator phase error, nor trajectory
straightness.
59
I. First integral scans after tune shim installation
13 mm gap
500
Phase = HP
Ix
Iy
400
Gap = 13mm
Iy calculated
Iy Sum
First Integrals (Gcm)
300
200
100
0
-100
-200
Local fit of order: 3
2-pole [Gcm] = 57.488
4-pole [G] = 258.31
6-pole [G/cm] = 44.223
Local fit of order 3
2-pole
[Gcm] = 68.059
-300
4-pole [G] = 1142.5
6-pole [G/cm] = -336.66
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Transverse position (cm)
Figure 84 First integrals at 13 mm gap. HP mode. Also shown is the calculated
dynamic effect, and the sum of the measured and dynamic effect.
60
2.5
1000
Phase = CP+ Gap = 13mm
Ix
Iy calculated
800
Iy
Iy Sum
600
First Integrals (Gcm)
400
200
0
-200
-400
-600
-800
Local fit of order: 3
2-pole [Gcm] = 40.359
4-pole [G] = -518.51
6-pole [G/cm] = 174.16
Local fit of order: 3
2-pole [Gcm] = 40.222
4-pole [G] = 1840
6-pole [G/cm] = 188.09
-1000
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
Transverse position (cm)
Figure 85 First integrals at 13 mm gap. CP+ mode. Also shown is the calculated
dynamic effect, and the sum of the measured and dynamic effect.
1200
1000
800
Phase = CP- Gap = 13mm
Ix
Iy calculated
Iy
Iy Sum
First Integrals (Gcm)
600
400
200
0
-200
-400
-600
-800
-1000
-1200
Local fit of order: 3
2-pole [Gcm] = 93.369
4-pole [G] = -493.37
6-pole [G/cm] = 80.619
-2.5
-2.0
-1.5
Local fit of order: 3
2-pole [Gcm] = 94.105
4-pole [G] = 1874
6-pole [G/cm] = 46.752
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Transverse position (cm)
Figure 86 First integrals at 13 mm gap. CP+ mode. Also shown is the calculated
dynamic effect, and the sum of the measured and dynamic effect.
61
2.5
Phase = VP
Ix
Iy
1500
Gap = 13mm
Iy calculated
Iy Sum
First Integrals (Gcm)
1000
500
0
-500
-1000
Local fit of order 3
2-pole [Gcm] = 10.237
4-pole [G] = -1677.1
6-pole [G/cm] = 1534.2
Local fit of order: 3
-1500 2-pole [Gcm] = 62.588
4-pole [G] = 4139.6
6-pole [G/cm] = -681.11
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
Transverse position (cm)
Figure 87 First integrals at 13 mm gap. VP mode. Also shown is the calculated
dynamic effect, and the sum of the measured and dynamic effect.
30 mm gap
250
Phase = HP
Ix
Iy
200
Gap = 30mm
Iy calculated
Iy Sum
First Integrals (Gcm)
150
100
50
0
-50
-100
-150
Local fit of order: 3
2-pole [Gcm] = 49.181
4-pole [G] = 121.36
6-pole [G/cm] = -4.2795
-200
-250
-2.5
-2.0
-1.5
-1.0
Local fit of order: 3
2-pole [Gcm] = 49.611
4-pole [G] = 164.92
6-pole [G/cm] = -13.659
-0.5
0.0
0.5
1.0
1.5
2.0
Transverse position (cm)
Figure 88 First integrals at 30 mm gap. HP mode. Also shown is the calculated
dynamic effect, and the sum of the measured and dynamic effect.
62
2.5
350
300
250
Phase = CP+ Gap = 30mm
Ix
Iy calculated
Iy
Iy Sum
200
First Integrals (Gcm)
150
100
50
0
-50
-100
-150
-200
Local fit of order: 3
2-pole [Gcm] = 68.927
4-pole [G] = 367.17
6-pole [G/cm] = 7.0893
-250
Local fit of order: 3
2-pole
[Gcm] = 68.899
-300
4-pole [G] = -216.16
-350 6-pole [G/cm] = 7.145
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
Transverse position (cm)
Figure 89 First integrals at 30 mm gap. CP+ mode. Also shown is the calculated
dynamic effect, and the sum of the measured and dynamic effect.
350
Phase = CPIx
Iy
300
250
Gap = 30mm
Iy calculated
Iy Sum
200
First Integrals (Gcm)
150
100
50
0
-50
-100
-150
Local fit of order: 3
2-pole [Gcm] = 85.94
4-pole [G] = -223.35
6-pole [G/cm] = -17.218
-200
-250
-300
-350
Local fit of order: 3
2-pole [Gcm] = 85.968
4-pole [G] = 359.97
6-pole [G/cm] = -17.274
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Transverse position (cm)
Figure 90 First integrals at 30 mm gap. CP- mode. Also shown is the calculated
dynamic effect, and the sum of the measured and dynamic effect.
63
2.5
400
Phase = VP
Ix
Iy
Gap = 30mm
Iy calculated
Iy Sum
First Integrals (Gcm)
300
200
100
0
-100
-200
-300
Local fit of order: 3
2-pole [Gcm] = 72.633
4-pole [G] = 50.225
6-pole [G/cm] = 10.342
-2.5
-2.0
-1.5
Local fit of order: 3
2-pole [Gcm] = 72.661
4-pole [G] = 633.55
6-pole [G/cm] = 10.287
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Transverse position (cm)
Figure 91 First integrals at 30 mm gap. VP mode. Also shown is the calculated
dynamic effect, and the sum of the measured and dynamic effect.
64
2.5
J. Hall probe scans on the undulator axis(13 mm gap)
HP Mode
Figure 92 The electron orbits for a 3 GeV electron at 13 mm gap for x = y = 0(HP
Mode).. The horizontal orbit averaged over one undulator period is also shown. After
tuneshim installation
65
CP+ Mode
80
Gap = 13 mm: CP+ mode
Vertical orbit
Horizontal orbit
60
Electron orbits
40
20
0
-20
-40
-60
-80µm
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Figure 93 The electron orbits for a 3 GeV electron at 13 mm gap for x = y = 0(CP+
Mode).. The horizontal orbit averaged over one undulator period is also shown.
CP- Mode
80
Gap = 13 mm: CP- mode
60
Vertical orbit
Horizontal orbit
Electron orbits
40
20
0
-20
-40
-60
-80µm
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
Longitudinal position (m)
Figure 94 The electron orbits for a 3 GeV electron at 13 mm gap for x = y = 0(CPMode).. The horizontal orbit averaged over one undulator period is also shown.
66
K. Analysis of peak field rolloff
For this device, there was some emphasis on the peak field rolloff performance. During the
conceptual design stage, we optimized the exact block dimensions, to improve the derivative in
the field roll off, from 500G/cm to below 400 G/cm. The field roll off was evaluated by locally
scanning over several poles, in the x-direction.
CP mode(13 mm gap)
-0.730
-0.730
-0.740
-0.740
-0.745
-0.745
-0.750
-0.750
Vertical field (T)
Vertical field (T)
Phase = CP+ Gap = 13mm
Pole 3
Fit
Pole 9
Fit
Pole 15
Fit
Pole 21
Fit
Pole 27
Fit
-0.735
-0.735
-0.755
-0.760
-0.765
-0.755
-0.760
-0.765
-0.770
-0.770
Phase = CP- Gap = 13mm
Pole 3
Fit
Pole 9
Fit
Pole 15
Fit
Pole 21
Fit
Pole 27
Fit
-0.775
-0.780
-0.785
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
x (cm)
0.5
-0.775
-0.780
1.0
1.5
2.0
2.5
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
x (cm)
0.5
1.0
1.5
2.0
2.5
Figure 95 Field roll off
500
500
Phase = CP- Gap = 13mm
Pole 3
Pole 21
Pole 9
Pole 27
Pole 15
300
300
200
200
100
0
-100
100
0
-100
-200
-200
-300
-300
-400
-400
-500
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Phase = CP+ Gap = 13mm
Pole 3
Pole 21
Pole 9
Pole 27
Pole 15
400
First gradients (G/cm)
First gradients (G/cm)
400
2.0
-500
-2.5
2.5
-2.0
-1.5
-1.0
-0.5
x (cm)
0.0
0.5
1.0
1.5
2.0
2.5
x (cm)
Figure 96 First derivative of field roll-off.
1600
1200
1200
800
800
Second gradients (G/cm^2)
Second gradients (G/cm^2)
1600
400
0
-400
-800
0
-400
-800
Phase = CP- Gap = 13mm
Pole 3
Pole 21
Pole 9
Pole 27
Pole 15
-1200
-1600
-2.5
400
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
Phase = CP+ Gap = 13mm
Pole 3
Pole 21
Pole 9
Pole 27
Pole 15
-1200
-1600
-2.5
2.5
x (cm)
-2.0
-1.5
-1.0
-0.5
0.0
x (cm)
Figure 97 Second derivative of field roll-off.
67
0.5
1.0
1.5
2.0
2.5
L. Reproducibility of the magnetic array
In this section, we present some investigations of the reproducilibity of the magnetic array, upon
the phasing motion. As is clear from the conceptual design report, the magnetic force vectors for
this structure are very large, the force vectors change direction upon phasing.
We have investigated, at minimum gap, the reproducibility of the circular polarization mode, after
travelling to the HP mode, and back again. We can study the average magnetic taper and see if it
changes at all. This can be done for both the vertical and horizontal field, based on the value of
the peak field at each pole. We see little change in both the average peak field as well as the
average magnetic taper.
Figure 98 Magnetic taper fit, based on vertical peak fields measured at each pole
68
0.70
CP+ mode
Horizontal Peak field, Bx
Linear fit
0.65
Peak fields (T)
0.60
0.55
0.50
0.45
0.40
0.35
0
2
4
6
8
10
12
14
16
18
Pole number
20
22
24
26
28
30
Figure 99 Magnetic taper fit, based on horizontal peak fields measured at each pole
Table 9 Summary of horizontal peak field taper upon phasing from CP+
Scan
number
Motion
Av.Peak
field
Av.
Taper(/pole)
1
CP+ to HP to CP+
0.73245
-9.925e-005
2
CP+ to HP to CP+
0.73248
-9.9445e-005
3
CP+ to HP to CP+
0.73217
-9.8275e-005
4
CP+ to HP to CP- to CP+
0.73206
-9.4014e-005
69
Table 10 Summary of vertical peak field taper upon phasing from CP+
Scan
number
Motion
Av.Peak
field
Av. Taper
1
CP+ to HP to CP+
0.73304
-0.00011778
2
CP+ to HP to CP+
0.7331
-0.00011969
3
CP+ to HP to CP+
0.73285
-0.00011733
4
CP+ to HP to CP- to CP+
0.73305
-0.00011491
Table 11 Summary of horizontal peak field taper upon phasing from CP-
Scan
number
Motion
Av.Peak
field
Av.
Taper(/pole)
1
CP- to HP to CP-
0.73459
-0.00030956
2
CP- to HP to CP-
0.73463
-0.0003103
3
CP- to HP to CP-
0.73448
-0.00030806
70
Table 12 Summary of vertical peak field taper upon phasing from CP-
Scan
number
Motion
Av.Peak
field
Av.
Taper(/pole)
1
CP- to HP to CP-
0.72996
0.00019122
2
CP- to HP to CP-
0.73013
0.0001864
3
CP- to HP to CP-
0.73002
0.00018925
We also examined the effect on the phase error at 30 mm gap, when changing gaps from 13 mm
to 30 mm, as compared to changing gaps from 40 mm to 30 mm. The phase error, in each case,
is shown in Figure 100, and summarized in Table 13. We see no discernible change in the
magnetic results which could indicate mechanical hysteresis of any kind.
10
Phase error Bx and By (degree)
Effect on phase error, upon gap change
Bx Phase Error 40-30 mm
Bx Phase Error 13-30 mm
5
0
-5
-10
0
5
10
15
Pole number
20
25
Figure 100 Phase error, in the VP mode, at 30 mm gap, upon gap change from 13 mm
and 40 mm.
71
Table 13 Summary of vertical peak field taper upon changing gap( VP mode)
Scan
number
Motion
Phase error
Av.
field
1
13 mm to 30 mm
3.84
0.474168
2
40 mm to 30 mm
3.83
0.474175
Peak
M. Correction coils HP mode
We have calibrated the coils in the HP mode at different gaps. Due to the close to unit
permeability of the magnet material, we expect little effect of moving the undulator phase.
There are 12 vertical windings and 8 horizontal windings. We see little multipole content coming
from the coils. The signal coming from the horizontal coil is quite weak, which means that the
uncertainty, at the smallest gap, becomes comparable to the signal itself.
Vertical coils
Figure 101 Second vertical integral data when upstream and downstream coils are
powered with +10 A
72
Figure 102 Second vertical integral data when upstream and downstream coils are
powered with -10 A
Horizontal coils
Figure 103 Second horizontal integral data when upstream and downstream coils are
powered with +10 A
73
Figure 104 Second horizontal integral data when upstream and downstream coils are
powered with +10 A
General Comments
N. Mounting of the permanent magnets and the shimming
process
The magnetic blocks mounted on the device, were received from Arnold Magnetics. They were
all within the magnetic specifications, as presented by Arnold Magnetics using a Helmholtz
system. In order to gain the strongest possible magnets, we chose isostatically pressed magnets,
as opposed to transverse die pressed magnets. In this manner, Arnold Magnetics were able to
provide magnets with a minimum closed circuit remanence above the specified 1.06 T.
74
Figure 105 Remanence data obtained from Arnold magnetics
75
Figure 106 Remanence data from Arnold magnetics
Due to our 3+1 keeper design, the magnets had to be divided into several different populations,
prior to being mounted into the keepers. The magnets for the B-keepers, which consist of two
opposing vertical magnets, along with a horizontal block, were chosen such that the magnetic
misorientation of the vertical magnets were minimized. Care was also taken to ensure that the
remanence of the magnets in the module were similar, in order to minimize the observed phase
error.
The field integral contributions of the A and B modules were all measured for -50  x  50 mm in
steps of 1 mm with the center of the flip coil 6.5 mm from the magnets. These field integral
contributions are loaded into a database. This database takes care of block rotations and block
flips such that the measured data is modified according to position on the undulator. Sample
integral contributions are shown in Figure 107.
76
Figure 107 Sample field integral contributions shown for different magnet blocks.
The first period was mounted on the girder starting on the upper girder at one end. After
mounting one period the field integrals were measured 6.5 mm from the magnets and the next
period, consisting of an A+B- module set, was selected in order to minimize the field integral
variations. The Hall bench was used to ensure accurate positioning and alignment of each
module. Finally both end sections were selected and mounted.
The device mas shimmed mainly by shimming magnetic poles in B-modules,as well as a little
module swapping.
The swapping and shimming process consisted initially of trajectory
straightening, and then of multipole corrections. Magic finger corrections were applied to
minimize the integral multipoles. These, however, do not correct phase dependent integrals.
O. Conclusion
We have here presented the final results of the magnetic measurement test of the SSRL 140 mm
Apple-II undulator. The details of the measurement setup have been described and the
reproducibility of the Hall probe bench and the flip coil bench have been documented. From the
Hall probe x and y-scans it has been documented that the undulator was well aligned.
The magnetic on-axis properties have been measured as a function of the gap. It was found that
the undulator period is 139.98 mm. The electron straightness and electron phase error is quite
good, as function of gap and phase. Unfortunately, the undulator does not meet the field
specification which concerns the minimum photon energy. We designed the device to have a
minimum photon energy of 6.7 eV, in the circular polarization phase, but ended up with 7.4 eV,
corresponding to several percent of peak field loss. We have performed detailed simulations, to
check if, in fact, there was some risk of demagnetization, in one of the phases but this was not
found to be the case. The calibration of the probe, has also been checked against a commercial
Group3 teslameter, which indicated that the calibration of the vertical field was fine. We also
experience a phase dependent multipole effect, which means that we are slightly off-spec in the
integral specification, due to a rapid field fluctuation near the undulator axis.
77
It was found that tune correctors could be implemented with minimal effect on the skew
integrals, and small effect on the electron trajectory, and electron phase error.
78